Skip to main content
SpringerLink
Log in

Cutting Force Modeling: Genesis, State of the Art, and Development

  • Chapter
  • First Online:
Mechanical and Industrial Engineering

Part of the book series: Materials Forming, Machining and Tribology ((MFMT))

Abstract

The chapter gives a historical prospective of the origin and developments of empirical equations for cutting force in the manner never presented before. It is shown that the Wiebe formula published in 1858 is still in wide use today in many research and practical applications including cutting tool manufacturers’ technical guides/catalogs. The chapter analyses the historical development of the formula for the cutting force from 1858 to the preset. The foundation of the so-called mechanistic approach in metal cutting is considered. It is discussed that there are actually two considerably different mechanistic approaches used today. Although both include the use of the cutting force coefficient, the way these coefficients are determined through numerous cutting tests are considerably different. The origin, essence, and drawbacks of both approaches are analyzed in great details. The chapter argues that no further progress in meatal cutting in terms of increasing its efficiency can be made if the known approach are used. The chapter suggests that at present stage of development, finite element method (FEM) modeling is one of feasible alternative to pure experimental studies in metal cutting. The problems to be addressed in FEM simulation in metal cutting as the proper model of metal cutting, relevant constitutive model of work material behavior, and contact conditions at the chip-rake face and workpiece-flank face interfaces are revealed and the feasible ways of their resolution are suggested discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is interesting to point out that all the papers by Friedrich on metal cutting and on gears start with the word “Ueber” (about).

  2. 2.

    Arguing with Nicolson about the influence of the (uncut) chip thickness, Taylor wrote “We have gone to great length in the paper to make it clear that it is the thickness of the chip which is the main factor, in allowing high cutting speeds for tools with broad cutting edges. And yet, Mr. Nicolson claims theta neither the thickness of the chip not the shape of the cutting edge of the tool need to be particularly considered in the problem”.

References

  1. Astakhov VP (2014) Drills: science and technology of advanced operations. CRC Press, Boca Raton, FL

    Google Scholar 

  2. Astakhov VP, Outeiro J (2019) Importance of temperature in metal cutting and its proper measurement/modeling. In: Davim PJ (ed) Measurement in machining and tribology. Springer, London, pp 1–47

    Google Scholar 

  3. Wiebe FKH (1885) Die Maschinen-Baumaterialien Und Deren Bearbeitung. Kessinger Publishing, LLC, Berlin (reprint 2010)

    Google Scholar 

  4. Time I (1870) Resistance of metals and wood to cutting. Dermacow Press House, St. Petersbourg, Russia (in Russian)

    Google Scholar 

  5. Zvorykin KA (1893) On the force and energy needed to separate the chip from the workpiece (in Russian). Russian Typo-Litography, Moscow, pp 57–96

    Google Scholar 

  6. Merchant ME (1944) Basic mechanics of metal cutting process. J Appl Mech 11:A168–A175

    Article  Google Scholar 

  7. Merchant ME (1945) Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip. J Appl Phys 16:267–275

    Google Scholar 

  8. Backer WR, Marshall ER, Shaw MC (1952) Size effect in metal cutting. Trans Am Soc Mech Eng 74:61–72

    Google Scholar 

  9. Taylor FW (1907) On the art of cutting metals. Trans ASME 28:70–350

    Google Scholar 

  10. Boston OW (1926) The elements of metal cutting. Ann Arbor, MI: University of Michigan Press

    Google Scholar 

  11. Nicolson JT (1904) Experiments with lathe-tool dynamometer. Trans ASME 23:883–935

    Google Scholar 

  12. Okoshi M, Fukui S (1933) Researshes on the cutting action of planning tool, by microkinetographic, photoelastic and piezoelectric methods. Sci Papaes Inst Phys Chem Res 22:97–166

    Google Scholar 

  13. Bricks AA (1896) Metal cutting (planing). MM Stasucevich Publ. House, St.Petersburg

    Google Scholar 

  14. Kronenberg M (1923) Grundzüge der Zerspanungslehre. Springer, Berlin

    Google Scholar 

  15. Kronenberg M (1966) Machining science and application: theory and practice for operation and development of machining processes. Pergamon Press, Oxford, New York

    Google Scholar 

  16. Friedrich H (1909) Ueber den Schnittwiderstand bei der Bearbeitung der Metalle durch Abheben von Spänen (in German). Z VDI 58(23):860–866

    Google Scholar 

  17. Friedrich H (1930) Ueber die Zerspanungstheorie (in German). Maschinenbau 2:47–51

    Google Scholar 

  18. Zorev NN (1966) Metal cutting mechanics. Pergamon Press, Oxford

    Google Scholar 

  19. Ripper W, Burley GW (1913) Cutting power of lathe turning tools. Proc Inst Mech Eng 85:1067–1210

    Google Scholar 

  20. Hippler W (1918) Die Dreherei und ihre Werkzeuge: in der neuzeitlichen Betriebsführung (in German). Springer, Berlin

    Google Scholar 

  21. Hippler W (1923) Die Dreherei und ihre Werkzeuge: in der neuzeitlichen Betriebsführung (in German). 3rd ed, vol 1. Julius Springer, Berlin

    Google Scholar 

  22. Klopstock H (1923) Untersuchung der Dreharbeit. Julius Springer, Berlin

    Google Scholar 

  23. Kurrein MAdS (1905) Aufbau der Schnelldrehspäne. Wien: Öst. Wschr. öffentl. Baudienst

    Google Scholar 

  24. Schlesinger G, Kurrein M (1924) Der Ausbau der Einrichtung das Versuchsfeldes für Werkzeugmaschinen an der Technischen Hochschule zu Berlin seit 1912. Springer Berlin Heidelberg, Berlin

    Google Scholar 

  25. De Leeuw AL, Plainfield NG (1917) A foundation for machine-tolol design and construction. ASME Trans 39:185–211

    Google Scholar 

  26. Cheluskin AN (1933) Cutting theory (in Russian). Gosmashmet, Moskow

    Google Scholar 

  27. Discussion on machinability: at the conference at the institution on 24th May 1946. Proc Inst Mech Eng. 155(1):267–291

    Google Scholar 

  28. Wallichs A (1930) Der heutige Stand der Forschung auf dem Gebiete der Metalzerspanug, in Berichte über betriebswirtschaftliche Arbeiten. Berlin, VDI-Verlag

    Google Scholar 

  29. Groover MP (2010) Fundamentals of modern manufacturing. materials, Processes, and Systems. 4th ed. Willey, Hoboken, NJ

    Google Scholar 

  30. Boothroyd G, Knight WA (2006) Fundamentals of machining and machine tools, 3rd edn. CRCPress, Boca Raton

    Google Scholar 

  31. Shaw MC (2005) Metal cutting principles, 2nd edn. Oxford University Press, Oxford

    Google Scholar 

  32. Klocke F (2011) Manufacturing processes 1. Csutting. Springer, Berlin

    Google Scholar 

  33. Kienzle O (1952) Die Bestimmung von Kräften und Leistungen an spanendenWerkzeugen und Werkzeugmaschinen. VDI-Z 94(11/12):299–305

    Google Scholar 

  34. Kienzle O, Victor H (1957) Spezifische schnittkräfte bei der metallbearbeitung. Werkstattstechnik und Maschinenbau 47(5):224–225

    Google Scholar 

  35. Isakov E (2004) Engineering Formulas for Metalcutting. Industrial Press, New York

    Google Scholar 

  36. Machining Data Handbook (1980) Machinability Data Center, Cincinnati, OH

    Google Scholar 

  37. McCauley CJ (ed) (2000) Machinery's Handbook. 26th ed. Industrial Press, New York

    Google Scholar 

  38. Sandvik coromant: cutting formulas and definitions. general turning. Available from: https://www.sandvik.coromant.com/en-us/knowledge/machining-formulas-definitions/pages/general-turning.aspx

  39. Sandvik coromant: specific cutting force. Available from: https://www.sandvik.coromant.com/en-gb/knowledge/materials/pages/specific-cutting-force.aspx

  40. Sandvik coromant: workpiece materials. Available from: https://www.sandvik.coromant.com/en-us/knowledge/materials/pages/workpiece-materials.aspx

  41. Sumitomo techical guidace reference N11 to N41. Available from: https://www.sumitool.com/en/downloads/cutting-tools/general-catalog/assets/pdf/GC_N2_en.pdf.

  42. Tangaloy: User's Guide. Available from: https://www.tungaloy.com/wp-content/uploads/GC_2018-2019_EE_G_User'sGuide.pdf.

  43. ISKAR: on-line cutting force calculator. Available from: https://mpwr.iscar.com/Turning/MachiningPower/Longitudinal/StraightEdge

  44. Taylor FW (1911) The principles of scientific management. Haper & Brothers, New York

    Google Scholar 

  45. ISCAR (2019) Coplete Machning Solution, non-rotating tool lines

    Google Scholar 

  46. Walter (2019) Perform line—economic, reliable, highest quality

    Google Scholar 

  47. Kennametal (2018) Master Cataloh 2018. Volume one—turning

    Google Scholar 

  48. Materials M (2019) Coated carbide (CVD) selection guide. Available from: http://www.mitsubishicarbide.com/en/technical_information/tec_turning_tools/tec_turning_insert/tec_turning_grades/tec_turning_diacoat_cvd

  49. Salomon C (1928) Zur theorie des Fräsvorgandes Z. Ver Deut Ing 1619–1624

    Google Scholar 

  50. Vulf AM (1963) Metal cutting. State Publishing House of Science Literature, Moscow (in Russian)

    Google Scholar 

  51. Martellotti ME (1941) An analysis of the milling process. Trans ASME 63:677–700

    Google Scholar 

  52. Martellotti ME (1945) An analysis of the milling process II. Down milling. Trans ASME 67:233–251

    Google Scholar 

  53. Janota M, Kolar P, Sulika M (2019) Operational method for identification of specific cutting force during milling. MM Sci J Special Issue on HSM 2019:3250–3257

    Google Scholar 

  54. Sawin NN (1926) Theory of milling cutters. Mech Eng 46:1203–1209

    Google Scholar 

  55. Persons F (1923) Power requred for cutting metal. Trans ASME 45:193–227

    Google Scholar 

  56. Boston OW, Kraus CE (1932) The elements of milling. Trans ASME. 54:71–92

    Google Scholar 

  57. Fu HJ, DeVor RE, Kapoor SG (1984) A mechanistic model for prediction of the force system in face milling operations. ASME J Eng Ind 106:81–88

    Article  Google Scholar 

  58. Armarego EJA (1967) Machining with double cutting edge tools—I. Symmetrical triangular cuts. Int J Mach Tool Des Res 7:23–37

    Google Scholar 

  59. Armarego EJA (2000) The unified-generalized mechanics of cutting approach—a step towards a house of performance models for machining operations. Mach Sci Technol 4:319–362

    Article  Google Scholar 

  60. Augspurger T, Schraknepper D, Bergs T (2020) Experimental investigation of specific cutting forces and estimation of the heat partitioning under increasing tool wear in machining nickel-based super alloy IN 718. Prod Eng Res Devel 14:491–498

    Article  Google Scholar 

  61. Astakhov VP (2006) Tribology of metal cutting. Elsevier, London

    Google Scholar 

  62. Rozenberg AM, Eremin AN (1956) Elements of metal cutting theory. Machgiz, Moscow (in Russian)

    Google Scholar 

  63. Artamonov EV, Vasiljev LV, Uteshev MH (2012) Metal cutting and temperature factor (in Russian). TumenNGSU, Tumen, Russia

    Google Scholar 

  64. Altintas Y (2000) Modeling approaches and software for predicting the performance of milling operations at MAL-UBC. Mach Sci Technol 4(3):445–478

    Article  MathSciNet  Google Scholar 

  65. Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and cnc design, 2nd edn. Cambrige, New York

    Book  Google Scholar 

  66. Astakhov VP (2005) On the inadequacy of the single-shear plane model of chip formation. Int J Mech Sci 47:1649–1672

    Article  MATH  Google Scholar 

  67. Reuleaux F (1900) Über den Taylor Whiteschen Werkzeugstahl Verein sur Berforderung des Gewerbefleissen in Preussen. Sitzungsberichete 79(1):179–220

    Google Scholar 

  68. Atkins AG, Mai Y-W (1985) Elastic and plastic fracture. Ellis Horwood, Chichester, UK

    Google Scholar 

  69. Atkins AG (2009) The science and engineering of cutting. Butterworth-Heinemann, Oxford UK

    Google Scholar 

  70. Atkins AG (2003) Modelling metal cutting using modern ductile fracture mechanics: qualitative explanations for some longstanding problems. Int J Mech Sci 45:373–396

    Article  Google Scholar 

  71. Astakhov VP (1998/1999) Metal Cutting Mechanics. CRC Press, Boca Raton, USA

    Google Scholar 

  72. Komarovsky AA, Astakhoy VP (2002) Physics of strength and fracture control: fundamentals of the adaptation of engineering materials and structures. CRC, Boca Raton

    Google Scholar 

  73. Sidjanin L, Kovac P (1997) Fracture mechanisms in chip formation processes. Mater Sci Technol 13(5):439–444

    Article  Google Scholar 

  74. Williams JG, Patel Y, Blackman BRK (2010) A fracture mechanics analysis of cutting and machining. Eng Fract Mech 77(2):293–308

    Article  Google Scholar 

  75. Williams JG, Patel Y (2016) Fundamentals of cutting. Interface Focus 6(3):20150108

    Article  Google Scholar 

  76. Cheng W, Outeiro J, Costes J-P, M'Saoubib R, Karaounic H, Astakhov VP (2019) A constitutive model for Ti6Al4V considering the state of stress and strain rate effects. Eng Fract Mech 219:103103

    Google Scholar 

  77. Xu X, Outeiro J, Shang J, Hu B, Zhao W, Astakhov V (2021) Machining simulation of ti6al4v using coupled Eulerian-Lagrangian approach and a constitutive model considering the state of stress. Simul Model Pract Theory 110:102312

    Google Scholar 

  78. Denkena B, Tonshoff HK (2011) Spanen Grudlagen. Springer, Berlin

    Book  Google Scholar 

  79. Awerjcewicz J (ed) (2011) Numerical analysis, theory and application. InTech: Rijeka, Croatia

    Google Scholar 

  80. Roth S, Chamoret D, Badin J, Imbert JR, Gomes S (2011) Crash FE simulation in the design process—theory and application. In: Awerjcewicz J (ed) Numerical analysis, theory and application. InTech: Rijeka, Croatia

    Google Scholar 

  81. Roll K (2008) Simulation of sheet metal forming—necessary developments in the future. In: The 7th international conference and workshop on numerical simulation of 3d sheet metal forming processes (NUMISHEET). Interlaken, Switzerland

    Google Scholar 

  82. Astakhov VP (2011) Authentication of FEM in metal cutting, chapter 1. In: Davim JP (ed) Finite element method in manufacturing processes. Wiley, pp 1–43

    Google Scholar 

  83. Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55:383–405

    Article  MathSciNet  MATH  Google Scholar 

  84. Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55:1017–1040

    Article  MathSciNet  MATH  Google Scholar 

  85. Borden MJ, Hughes TJ, Landis CM, Anvari A, Lee IJ (2016) A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng 312:130–166

    Article  MathSciNet  MATH  Google Scholar 

  86. Eldahshan H, Bouchard P-O, Alves J, Perchat E, Munoz DP (2021) Phase field modeling of ductile fracture at large plastic strains using adaptive isotropic remeshing. Comput Mech 67:763–783

    Article  MathSciNet  MATH  Google Scholar 

  87. Abacus 6.11 manual

    Google Scholar 

  88. Astakhov VP (2018) Mechanical properties of engineering materials: relevance in design and manufacturing. In: Davim P (ed) Introduction to mechanical engineering. Springer International Publishing AG, Cham, Switzerland, pp 3–41

    Google Scholar 

  89. Liu J, Bai Y, Xu C (2013) Evaluation of ductile fracture models in finite element simulation of metal cutting processes. J Manuf Sci Eng 136:011010; Evaluation of ductile fracture models in finite element simulation of metal cutting processes. J Manuf Sci Eng 136:011010

    Google Scholar 

  90. Astakhov VP, Xiao X (2016) The principle of minimum strain energy to fracture of the work material and its application in modern cutting technologies. In: Davim P (ed) Metal Cutting Technology. De Gruyter Publishers, Boston, MA, pp 1–35

    Google Scholar 

  91. Abushawashi Y, Xiao X, Astakhov V (2017) Practical applications of the “energy–triaxiality” state relationship in metal cutting. Mach Sci Technol Int J 21(1):1–18

    Article  Google Scholar 

  92. Abushawashi Y, Xiao X, Astakhov VP (2013) A novel approach for determining material constitutive parameters for a wide range of triaxiality under plane strain loading conditions. Int J Mech Sci 74:133–142

    Article  Google Scholar 

  93. Wang B, Xiao X, Astakhov VP, Liu Z (2019) The effects of stress triaxiality and strain rate on the fracture strain of Ti6Al4V. Eng Fract Mech 219:106627

    Google Scholar 

  94. Klocke F (2013) Manufacturing processes 4 forming. Springer Heidelberg, New York

    Google Scholar 

  95. Joun MS, MG, Moonc HG, NG., Choi, I.S., Lee MC, Jun BY (2009) Effects of friction laws on metal forming processes. Tribology Int 42:311–319

    Google Scholar 

  96. Kim H, Kardes N, Chapter 7: friction and lusbrication. In: Altan T, Tekkaya AE (eds) Sheet Metal forming—fundamentals. ASM International: Novelty, OH

    Google Scholar 

  97. Astakhov VP, Shavets SV (2020) Technical resource of the cutting wedge is the foundation of the machining regime determination. Int J Manuf Mater Mech Eng 10:1–17

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Production Service Management Inc, 1792 Elk Lane, Okemos, 48864, USA

    Viktor P. Astakhov

Authors
  1. Viktor P. Astakhov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal

    J. Paulo Davim

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Astakhov, V.P. (2022). Cutting Force Modeling: Genesis, State of the Art, and Development. In: Davim, J.P. (eds) Mechanical and Industrial Engineering. Materials Forming, Machining and Tribology. Springer, Cham. https://doi.org/10.1007/978-3-030-90487-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-90487-6_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-90486-9

  • Online ISBN: 978-3-030-90487-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation